Rank varieties and 𝜋-points for elementary supergroup schemes

Benson, Dave; Iyengar, Srikanth; Krause, Henning; Pevtsova, Julia

doi:10.1090/btran/74

Rank varieties and $\pi$-points for elementary supergroup schemes
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by Dave Benson, Srikanth B. Iyengar, Henning Krause and Julia Pevtsova HTML | PDF

Trans. Amer. Math. Soc. Ser. B 8 (2021), 971-998

Abstract:

We develop a support theory for elementary supergroup schemes, over a field of positive characteristic $p\geqslant 3$, starting with a definition of a $\pi$-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and $\pi$-points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra $k[t,\tau ]/(t^p-\tau ^2)$, where $t$ has even degree and $\tau$ has odd degree. The strength of the theory is demonstrated by classifying the parity change invariant localising subcategories of the stable module category of an elementary supergroup scheme.

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